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Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures

Colin J. BushnellGuy Henniart — 2000

Journal de théorie des nombres de Bordeaux

Let F / p be a finite field extension. The Langlands correspondence gives a canonical bijection between the set 𝒢 F 0 ( n ) of equivalence classes of irreducible n -dimensional representations of the Weil group 𝒲 F of F and the set 𝒜 F 0 ( n ) of equivalence classes of irreducible supercuspidal representations of GL n ( F ) . This paper is concerned with the case where n = p m . In earlier work, the authors constructed an explicit bijection π : 𝒢 F 0 ( p m ) 𝒜 F 0 ( p m ) using a non-Galois tame base change map. If this tame base change satisfies a certain conjectured...

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